By George R. Kempf (auth.), Enrique Ramírez de Arellano (eds.)

ISBN-10: 3540469133

ISBN-13: 9783540469131

ISBN-10: 3540521755

ISBN-13: 9783540521754

From the contents:G.R. Kempf: The addition theorem for summary Theta functions.- L. Brambila: life of definite common extensions.- A. Del Centina, S. Recillas: On a estate of the Kummer sort and a relation among moduli areas of curves.- C. Gomez-Mont: On closed leaves of holomorphic foliations through curves (38 pp.).- G.R. Kempf: Fay's trisecant formula.- D. Mond, R. Pelikaan: becoming beliefs and a number of issues of analytic mappings (55 pp.).- F.O. Schreyer: definite Weierstrass issues occurr at so much as soon as on a curve.- R. Smith, H. Tapia-Recillas: The Gauss map on subvarieties of Jacobians of curves with gd2's.

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Additional info for Algebraic Geometry and Complex Analysis: Proceedings of the Workshop held in Pátzcuaro, Michoacán, México, Aug. 10–14, 1987

Example text

T i c , ble curve of genus complete locus W 41(F) Since A Its c a n o n i c a l the cuadrics in of ~I~(F) and 2 is r a m i f i e d ducible lar p o i n t ~ if at the A is. onds p a s s i n C trough correspond to the two p e n c i l s (a line) cone N quadric n: N ~ A the t a n g e n t ear series 6. InFI* of d i m e n s i o n rically the d i v i s o r c 6 N p. Since s deifnes phism, s(N) line to be the 2 which & A, is re- at a n o n s i g u - containing to F let o B. a singular quadric of N wl(F) '4 A.

From the diagram and the fact that ~ relation between Gauss if w e ) j(~) C ' J (C) is a l o c a l o ~ that , G = s o a' G: x" r~l* e'* seen in is i n j e c t i v e In o r d e r the morphism [acl* and map. 3) that a' ¢'*0E(U) ramified) the results of Beauville, i(~) ~ ~. 1. ® ~' the we need and so claim. 7. n*0H(1) ~ OE(U ® n). 8. Proof. ~'*(n*(0 the above Frorosition will follow from (i)) -~ ~X' Let us first observe volution, then j(g~) m': X' ~ IU G nl* ~ 2 that is m*(0 ~2(i)) = KX, - g~ . ~ QX' ' g~s So if we put n(E) the cone the p r o j e c t i o n with S' from ~, of the lines determined S' = Z' C H, 1 Therefore in- Hence when we consider t h e m o r p h i s m to prove Proposition x,x',x"EX' then there exists a line is the elliptic are lines tangent to the conic which is I U ® ~I* of enough to prove that if (as divisor l.

1. B of the s i n g u l a r [Te]. the v e r t e x of the reg induces on N a lin- poZar series: ~ E ~ consists A e at in p a r t i c u l a r s ~ 0~4(2) ~ aN ® H ®2 with of the passes restricted %Thich c o i n c i d e s geomet- to throuch N via the p o l a r nor- 41 where H = n*0A(1) ing to it cuts and o u t on for e a c h N (via point s) in ~ the c u a d r i c the F o l a r divisor correspond- of t h a t point. So we have: s*0 ]p4(1) where M ~ M ® H is a t h e t a - c h a r a c t e r i s t i c the r e s t r i c t i o n such that h°(N,M) = 0.

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Algebraic Geometry and Complex Analysis: Proceedings of the Workshop held in Pátzcuaro, Michoacán, México, Aug. 10–14, 1987 by George R. Kempf (auth.), Enrique Ramírez de Arellano (eds.)


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